Begin by preheating your oven to 375°F. Season each chicken breast with salt, paprika, and garlic powder. Place each breast between two sheets of plastic wrap and gently pound until about ¼-inch thick. This ensures even cooking and makes rolling easier.
Spread a thin layer of Dijon mustard onto each flattened piece. Lay one slice of ham on top, then place the folded Swiss cheese in the center. Roll each chicken breast tightly and secure with a toothpick so nothing falls out while cooking.
Set up your breading station using three shallow dishes. Coat each chicken roll first in flour, then dip into the beaten eggs, and finally press into the panko breadcrumbs until thoroughly coated.
Heat a thin layer of vegetable oil in a skillet over medium-high heat. Remove the toothpicks, then fry each roll until golden brown on all sides. Transfer to a rack set over a baking sheet and bake for 20–25 minutes until the chicken is cooked through.
Whisk lemon juice, vinegar, honey, grated garlic, salt, and pepper together, then slowly whisk in olive oil. Toss with mixed greens for a bright, fresh side.